developing a joint supply chain plan for the coal industry...

Scientia Iranica E (2021) 28(2), 877{891

Sharif University of TechnologyScientia Iranica

Transactions E: Industrial Engineeringhttp://scientiairanica.sharif.edu

Developing a joint supply chain plan for the coalindustry considering con ict resolution strategies

Y. Jianga;�, Q. Xub, and Y. Chenc

a. School of Management, Shenyang University of Technology, Shenyang 110870, China.b. MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing

100044, China.c. Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore 119077, Singapore.

Received 29 November 2017; received in revised form 6 May 2019; accepted 21 July 2019

KEYWORDSProduction anddistribution;Plan coordination;Con ict management;Model and algorithm;Coal industry.

Abstract. An integrated coordination planning problem pertaining to the energyenterprise aims to balance the plans submitted by the production and distribution branchesto mitigate the con ict between them. The conception of this research comes from thechallenges encountered in practice in the energy industry. Practical experience indicatesthat con icts occur commonly among the respective plans made by the production anddistribution branches. A plan coordinating approach is proposed that considers two aspects:maximizing company pro�t and minimizing the gap between the proposed plans andthe coordinating ones that implement a con ict resolution approach. We apply geneticalgorithm to handle this nonlinear optimization problem. A case study of the world'slargest coal supplier in China shows that if con icts occur in the original plans, the moste�ective method is to adjust the original plans from a global perspective, which has a strongrelationship with the overall interests. The proposed model can e�ectively neutralize thesecondary in uences of the con ict.

© 2021 Sharif University of Technology. All rights reserved.

1. Introduction

Preparation of a preoperational plan is good for supplychain systems to coordinate multiple producers, carri-ers, and distributors and advance the e�ciency of thementioned systems. The conception of this researchderives from the challenges encountered in practicefrom the viewpoint of the world's largest coal supplierin China. Its main business covers coal production,

*. Corresponding author. Tel.: +86 13889388168E-mail addresses: [email protected] (Y. Jiang);[email protected] (Q. Xu); [email protected] (Y.Chen)

doi: 10.24200/sci.2019.5671.1414

rail transportation, and power generation, as shownin Figure 1. The operation of numerous subsidiariesdepends on the planning management from the groupheadquarters. At the beginning of the planning stage,the production and distribution branches are requiredto submit their plans to the command center at thegroup's headquarters. Due to the separation andindependence of the business among the sub-branches,the occurrence of con icts is extremely common andit is not easy for the branches to overcome thesecon icts on their own. One should take the operationreport in February 2012 as an example, which indicatesa 40% gap between the production plan and thedistribution plan. According to the business report,in February 2016, the group company ran �fty coalmines and twenty-two types of coals were involved.

878 Y. Jiang et al./Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 877{891

Figure 1. Operation structure of the vertical integrationcompany.

Distribution areas cover thirteen provinces, cities, andregions and three customer categories are involved. Anumber of national, local, and owned railway lineshave participated in the operation. The number ofcorresponding constraints and variables in the model ishuge. Bhatnagar et al. [1] addressed the coordinationof multiple plants in terms of production planning in avertically integrated �rm and they identi�ed the criticalproblems that managers and researchers must addressto ensure that production and inventory decisions canbe determined in a manner optimal for the organizationas a whole.

Several examples of such scenarios exist at homeand abroad. In particular, in the industry, the modeof mass production, transportation, and distributionimposes a higher demand for plan management. An ex-ample is Broken Hill Proprietary Billiton Ltd. (BHP),whose corporate headquarters set the planning objec-tives and determine a balanced operation plan, whilethe secondary units are responsible for the decompo-sition and implementation [2]. Another example isCompanhia Vale do Rio Doce. Vale is a Brazilian multi-national corporation engaged in metals and mining andit is one of the largest logistics operators in Brazil.Vale is the largest producer of iron ore and nickel inthe world. The company also currently operates ninehydroelectricity plants and a large network of railroads,ships, and ports used to transport its products [3].Its headquarters are responsible for not only settingthe objectives and principles, determining a balancedoperation plan, performing comprehensive optimiza-tion, and providing the optimization plan, but alsocontrolling the operation plan. The secondary units actonly as business workshops, having lower autonomy.

Complex supply chain information generatedfrom multiple branches is no longer suitable to beprocessed only by experience. Time and manpowerconsumption are the main constraints. In this pa-per, a mathematical optimization method involvingan embedded con ict resolution strategy is proposedto solve this problem, as shown in Figure 2. In themathematical model, con icts information is re ectedas illogical constraints, implying that we cannot �nd

Figure 2. Process ow of planning operation.

feasible solutions using the original model. Therefore,some human interventions must be imposed on themodel to deal with con icts. The main measure em-bedded in our planning procedure is the application ofthe con ict resolution approach to achieve coordinationbetween the multiple plans of di�erent branches. Inthis process, we pay particular attention to the e�ect ofimplementation. It should be noted that the degree ofdissatisfaction of each branch is directly proportionalto the signi�cant di�erences existing between theirrespective plans and the plans formulated after con ictresolution. This factor must be taken into account inthe model through a quanti�ed method.

The remaining research is organized as follows.The proposed coordinating model is described in Sec-tion 3. A heuristic method employed for solving theproblem is presented in Section 4. In Sections 5 and6, a test network and a case study are presented tovalidate the model and algorithm.

2. Literature review

Given the conclusion drawn by Goyal and Gupta,the coordination between the buyer and supplier isgood for both sides [4]. In studies pertaining tothe supply chain, an increasing number of researchershave focused on the coordination of production anddistribution from strategic, tactical, or operationalperspectives [5]. In contrast, the research on theintegrated production-distribution scheduling problemis relatively recent, and it is termed as the integratedproduction-distribution planning or scheduling; thisdomain includes studies such as those of Pundoor andChen [6], Pornsing et al. [7], Zhong and Jiang [8],Russel et al. [9], Kishimoto et al. [10], Ma et al.[11], and Scholz-Reiter et al. [12]. In the modelspresented in some studies, for example, in Cheng etal. [13], Devapriya et al. [14], and Noroozi et al.[15], one or a combination of cost-based, time-based,and revenue-based performance measures is often seen

Y. Jiang et al./Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 877{891 879

as the goal of system optimization [16{23], and therelevant truck routes, eet size, job processing or batch-ing are seen as constraints. The literature pertainingto the methods employed to balance the respectiveplans of the di�erent branches in the integrated supplychain, aimed at minimizing the total global cost fromthe global perspective, is quite limited in scope. Atradeo� approach [11] is directed at determining theplants and warehouses that should operate to servecustomers with the total cost lying between the totalglobal cost and the costs in the respective branches.Sawik [24] merged production and distribution opera-tions by formulating a mathematical approach. Themajor decision-making involved determining whetherthe customer orders could be completed as plannedunder di�erent disruption scenarios or not; however,the speci�c quantity was not considered.

In production-distribution problems, collabora-tive cooperation as the core of supply chain man-agement will help the member units to achieve thewin-win purposes in a hierarchical system [25{27].Two contrasting objectives are included in the existingstudies that are speci�ed by di�erent branches such asreducing cost and improving service level. Consideringthat con ict of interest is a frequent and recurrentphenomenon in di�erent stakeholder groups, its rolein decision-making in the supply chain must be givendue attention [11]. These con icts, however, canresult in mutual in uences, and these mutual in uencesmay signi�cantly impact the production-distributionplanning. Many existing studies have focused onsolving the integrated production-distribution prob-lems using multi-objective programming and formu-lated di�erent goals and con icting objectives as multi-objective programming problem [28,29]. Similarly, thebi-level programming approach is used to formulatethose participants that belong to di�erent stakeholdergroups as two optimization problems, and the leaderdecisions at the top are constrained by the resultsof the follower [30{32]. This approach can eliminatecon icts and enhance coordination between the dif-ferent decision entities, which is vital for ensuringsupply chain e�ciency. However, di�erent decisionentities are dissatis�ed when large di�erences existbetween their respective plans and the ones formulatedafter con ict resolutions. Bilevel programming cannotmeasure such di�erences. Thus, we need to takethe expression of dissatisfaction into account in ourmodel as a quantitative measure. In our research,a novel con ict resolution approach is developed tocontrol the con ict resolution between the participantsin an integrated production-distribution planning prob-lem.

A few studies such as in Chen and Vairaktarakis[33], Chen and Lee [34], Xuan [35], and Zhong etal. [36] focused on production scheduling considering

the delivery process, in which the distribution opera-tions were mainly carried out by third-party carriers,with emphasis on road transportation with homoge-neous vehicles or the Vehicle Routing Problem (VRP).The collaboration of job processing and rail timetablefrom time dimension is one of the aspects that hasreceived insigni�cant attention [37]. Several similarresearches of production and transportation problemwere investigated by Moons et al. [38], Li and Li [39],Liotta et al. [40], and Azadian et al. [41].

3. Integrated scheduling model

Herein, a production and distribution network is con-sidered that consists of several production branchescombined in set I, self-owned railway and state-owned railway lines denoted by the set L, distributionbranches denoted by set J of demand nodes, set of coaltypes M , and classes of customers de�ned by the set N .Production branches I and distribution branches J arelocated in di�erent geographical areas, and the coal isdelivered though railway lines. The model is proposedto maximize the economic objective and minimize thepenalty cost due to con ict resolution considering con-strains of real production, transportation, and demand.

3.1. Symbol notationsFrom the viewpoint of our model, the manager ofthe integrated group company makes the followingdecisions:

(i) Determining the optimal coal types and output;

(ii) Selecting the best transport route;

(iii) Providing optimal matching relationships withthe customer requirements.

The variables in this paper are listed as follows:

Networki = 1; : : : ; I Production branchesjIj The total number of production

branchesj = 1; :::; J Distribution branchesjJ j The total number of distribution

branchesl = 1; :::; L Alternative transport routesjLj The total number of routesm = 1; :::;M Coal typesjM j The number of coal typesn = 1; :::; N Categories of customerjN j Is the number of customer categoriesk = 1; :::;K Transportation segments in dispatching

networkjKj The total number of segments


k(l) The set of segments included in theroute l

l(k) The set of routes via the segment k

Production branch[aim; �aim] Production plan in the range of aim to

�aim of production branch i for type m[0; Tim] Capacity of production branch i for

type m�Ai; �Ai

�Upper and lower bounds of productivityof production branch i

[0; Ti] Productivity of production branch icim Variable cost per unit of type m from

production branch ici Fixed production cost of production

branch iTransportation networkdk Capacity of segment ksk Length of segment kpk Transportation cost per ton-km of

segment k

Distribution branch�Bjmn; �Bjmn

�Demand plan in the range of Bjmnto �Bjmn from customer class n in thearea j for type m

[0; Tjmn] Largest demand size for customer classn for type m in the area j�

Bjn; �Bjn�

Demand plan from customer class n inthe area j in the range of Bjn to �Bjn

[0; Tjn] Demand size in the area j for customerclass n

pjmn Selling price in the area j for customerclass n, type m

cjm Selling cost in the area j for type m

Decision variablesxijmln Optimal amount from production

branch i to demand branch j usingroute l for customer class n and coaltype m

Yi If the production branch i operates,Yi = 1; otherwise, Yi = 0

3.2. Basic assumptionsTo facilitate the model formulation, we considered thatthe following assumptions would hold throughout thisstudy.

Assumption 1. A large uctuation will accrue ifthe scheduled cycle is short. In practice, the railwayvehicle turnover cycle is the key in uencing factor inthe scheduled cycle. Therefore, we de�ne the scheduledcycle to be longer than one day.

Assumption 2. Our research has been advancingfrom a strategic viewpoint, and the train dispatchingproblem, which is investigated in operational terms, isnot considered in the proposed model.

3.3. Model constraintsThe proposed model considers two types of constraints:hard and soft constraints. Hard constraints ensure thefeasibility of the coordination scheduling model, andsoft constraints control the quality of the results.

3.3.1. Hard constraintsAccording to Constraint (1), the freight volume cannotexceed the capacity of segment.X

i

Xj

Xm

Xl(k)

Xn

xijmln � dk 8k: (1)

Constraint (2) ensures the output for any productionbranch i, and coal type m must have adequate produc-tion such that the output can be larger than the lowerbound and must not have excessive production suchthat the output can be less than the upper bound.Thus, the following formula is utilized to determineand describe the capacity restriction for any productionbranch i 2 I, coal type m 2M :

0 � xim � Yi � Tim 8i;m; (2)

where:

xim =Xj

Xl

Xn

xijmln 8i;m: (3)

The total output of production branch i can be calcu-lated through Eq. (5). For any production branch i, thetotal output should satisfy the following expression:

0 � xi � Yi � Ti 8i; (4)

where:

xi =Xj

Xl

Xm

Xn

xijmln 8i: (5)

Di�erent demand areas are subject to a limit andshould satisfy Inequal. (6) for any demand area j,customer class n, and coal type m:

0 � xjmn � Tjmn 8j;m; n; (6)

where:

xjmn =Xi

Xl

xijmn 8j;m; n: (7)

The total demand in area j for the customer class nshould satisfy Inequal. (8), and it can be calculatedusing Eq. (9):

0 � xjn � Tjn 8j; n; (8)

where:

xjn =Xi

Xm

Xl

xijmln 8j; n: (9)


3.3.2. Soft constraints on productionFor any production branch i and coal type m, Inequals.(10) and (11) ensure that the respective productionplan will satisfy the requirements of each productionbranch. In practice, aim and �aim can be equal.

Yi � aim � xim � Yi � �aim 8i;m; (10)

Yi �Ai � xi � Yi � �Ai 8i: (11)

The logic con icts among the respective productionplans can be eliminated by introducing several slackvariables into Inequals. (10) and (11). Therefore,Inequals. (10) and (11) are reformulated into Inequals.(12){(17) and Eqs. (18) and (19). A slack variableensures that a feasible solution can be found even ifthe con icting constraints exist. Eqs. (18) and (19)ensure that the coordination of the plan can only go inone direction.

0�Yi � (aim+dim)�xim�Yi � (�aim+ �dim)�Tim8i;m; (12)

0 � Yi � (Ai+di) � xi�Yi � ( �Ai+ �di) � Ti 8i; (13)

�Yi � aim � dim � 0; (14)

�Yi �Ai � di � 0; (15)

0 � �dim � Yi � (Tim � �aim); (16)

0 � �di � Yi � (Ti � �Ai); (17)

�dim � dim = 0; (18)

�di � di = 0: (19)

3.3.3. Soft constraints on distributionFor any demand area j, coal typem, and customer classn, Inequals. (20) and (21) ensure that the respectivedistribution plans will satisfy the requirements of eachdistribution branch:

Bjmn � xjmn � �Bjmn 8j;m; n; (20)

Bjn � xjn � �Bjn 8j; n: (21)

Similarly, several slack variables are introduced into In-quals. (20) and (21) and we reformulate these equationsinto Inequals. (22){(25) and Eqs. (26) and (27):

0 �Bjmn + djmn � xjmn � �Bjmn + �djmn � Tjmn8j;m; n; (22)

0 � Bjn+djn�xjn� �Bjn+ �djn � Tjn 8j; n; (23)

djmn; djn � 0; (24)

�djmn; �djn � 0; (25)

�djmn � djmn = 0; (26)

�djn � djn = 0: (27)

3.4. Economic and coordinating objectivesA coordination scheduling model is proposed basedon the hard and soft constraints. Soft parameters �and �, which are the coe�cients used to balance themagnitude of the subobjective function, are introducedinto the two objectives.

Objective function = Max (income� selling cost

�cost of coordinated adjustment)

= max�(Z1 � Z2)� � �DBS: (28)

The income and selling costs can be formulated usingInequals. (23) and (24), respectively.

Z1 =Xj

Xm

Xn

pjmn �X

i

Xl

xijmln

!; (29)

Z2 =Xi

Xm

0@cim �Xj

Xl

Xn

xijmln

1A+Xj

Xm

cjm �X

i

Xl

Xn

xijmln

!+Xi

Xj

Xn

Xm

Xl(k)

pk � xijmln

+Xi

Yici: (30)

In practice, the coordination quality is measured bythe di�erence between the original plans and the �nalcoordinated ones. That is, the �nal coordinated plansare better if they involve less changes than the originalplans. Since the adjustments in the plans are measuredby the changes in the formulated plans compared to theoriginal plans, we obtain the coordinating objective asfollows:DBS =Z3 + Z4 + Z5 + Z6 =

Xi

Xm

(�� dim��+ jdimj)

+Xi

(�� di��+ jdij) +

Xj

Xm

Xn

(�� djmn��

+��djmn��) +

Xj

Xn

(�� djn��+

��djn��): (31)

4. Solution algorithm

The scale of the real problem is always relativelylarge. In order to ensure that the operation managers


can obtain a solution within a reasonable amountof time, we apply Genetic Algorithm (GA) to theproposed model. It has been successfully applied tomultiple related issues, e.g., integrated scheduling andrescheduling of railway transportation [37,42], VRPsolution [43], supply chain design problems [44], andtransportation scheduling problems [45]; besides, thee�ectiveness of the algorithm has been demonstrated.The procedure for the GA employed in this study issimilar to the general procedure, as de�ned in thefollowing steps:

1. The GA uses real-number encoding, and the en-coding structure of the chromosome is shown inFigure 3. The column indicates di�erent decisionvariables and each row indicates one solution. Toimprove the calculation e�ciency, infeasible in-formation concerning the initial samples must beexcluded. For example, the production branch acannot produce the coal type b according to itsnatural condition. Therefore, the element at thecolumn (i�j�m�n�l+ (a� 1)�m+ b) must be set to\0", that is, �dim = 0.

2. The quality of chromosomes is evaluated. In thisstep, the hard and soft constraints are absorbedinto the objective function, that is, the modelis transformed to correspond to an unconstrainedoptimization. The �tness function can be expressedas follows.

Fitness function = Income� selling cost

�hard constraints penalty � soft constraints

penalty � cost of coordinated adjustment

= � (Z1 � Z2)�Hard constraints� Soft

constraints� �� DBS: (32)

The hard constraints (Z7) can be de�ned as apenalty for a value that is not within the rangeof maximum and minimum values. Therefore, wecan resolve the following equation, where M is asu�ciently large positive number.

Hard constraints:

Z7 =M�max[0; �aim + �dim � T im] +M�max

[0;�aim � dim] +M�max[0; �Ai + �di � Ti]+M�max[0;�Ai � di] +M�max[0; �Bjmn

+ �djmn � Tjmn] +M�max[0;�Bjmn�djmn]

+M�max[0; �Bjn + �djn � Tjn]

+M�max[0;�Bjn � djn]

+M�max[0;Xi

Xj

Xm

Xl(k)

Xn

xijmln�dk]:(33)

Similarly, the soft constraints (Z8) can be formu-lated as follows:

Soft constraints:

Figure 3. Encoding style and solution expression of Genetic Algorithm (GA) chromosomes.


Z8 =M�max[0; xim � �aim � �dim]

+M�max[0; aim + dim � xim]

+M�max[0; xi � �Ai � �di]

+M�max[0; Ai + di � xi]+M�max[0; xjmn � �Bjmn � �djmn]

+M�max[0; Bjmn + djmn � xjmn]

+M�max[0; xjn � �Bjn � �djn]

+M�max[0; Bjn + djn � xjn]: (34)

3. The crossover and mutation operations are twomajor operations, which are shown in Figure 4, andthese operations can further improve the qualityof solutions and enrich the diversity of solutions.An arithmetic crossover process is applied to twochromosomes at a time and two new solutions canbe obtained using Eqs. (35) and (36):

Xp;j = Xp+1;j � rand + Xp;j � (1� rand); (35)

Xp+1;j = Xp;j � rand + Xp+1;j � (1� rand): (36)

We apply a nonuniform mutation process to onechromosome and a new solution can be obtainedusing Eqs. (37) and (38):

Xp;j =Xp;j�Xp;j�rand � (1�gen=maxgen)2; (37)

Xp;j =Xp;j+Xp;j�rand � (1�gen=maxgen)2: (38)

5. Discussion in a test network

We designed a test network including 7 points, 9segments, and 1 OD demand, as shown in Figure 5.The parameters of each segment are labeled on thesegment, representing, in order, the sequence number,length, capacity, and transportation cost per ton-kmin the sequence. We set i = 1, j = 1=, m = 2,n = 2, and l = 4. The related costs and prices aregiven in Table 1. Table 2 lists the upper and lower

Table 1. Related costs and prices (i = 1, j = 1).

n = 1 n = 2

m = 1 m = 2 m = 1 m = 2

Cjm 124 141 124 141Pjmn 511 658 475 607Cjm 5 5 5 5Ci 5000

Table 2. Original plans for production and distributionbranches.

Parameter Lowerbounds

Upperbounds

Maximumcapacity

aim 40 40 #Tim # # 50Ai 70 90 #Ti # # 100

Bjmn 15 20 #Tjmn # # 25Bjn 40 40 #Tjn # # 50

bounds for the production and distribution branches.For simplicity, we assume that:

a11 =a12; T11 =T12; B111 =B112 =B121 =B122;

T111 =T112 =T121 =T122; B11 =B12; and T11 =T12:

5.1. Optimal resultsThe experiment was applied to a personal computerfeaturing Intel Core i5, 2.60 GHz CPU, and 4 GBRAM. The population size is 100 and the iterationterminates 500 times. The crossover and mutationrates are 0.95 and 0.10, respectively. The parameter� in the objective is set to 1 and � = 200. Table 3presents the results of the experiment. The qualityof the scheduling coordination was controlled by theobjective. To attain a higher quality for coordinatedplans, slight changes were made.

A comparison between calculation results andthose of the other algorithms, such as GeneticAlgorithm-Simulated Annealing (GASA) and PSO, ismade, as shown in Table 4. Several conclusions can bederived as follows:

1. The lower bound is the condition in which theoriginal plans from all partners are used as the �nalplans instead of making adjustments. The optimalresults show that Ai is 80 and a11 = a12 = 40. Thedemand for any n is 40, that is, B11 = B12 = 40and T111 = T112 = T121 = T122 = 20. Allproducts can be digestive and all demands canbe satis�ed. The results show that the value ofthe hard constraints is 5:0�M = 5:0e + 10. Wemust refer to the network bottleneck section toprovide further explanation. The out ow capacityof the network is the summation of the capacities ofsegments 1 and 2, which is equal to 100. The in owcapacity of the network is the summation of thecapacities of segments 5, 6, and 7, being equal to75. Thus, the capacity of the network is determinedby the bottleneck section. The total supply anddemand are both 80; thus, there is a capacity gap


Figure 4. Process ow of the Genetic Algorithm (GA).


Table 3. Coordination results for the test network.

aim �aim Ai �Ai Bjmn �Bjmn Bjn �Bjn

d11

-1.73

�d11

0

d1

0

�d1

0 d1110 �d111

0

d11

-4.97

�d11

0

d1120 �d112

+0.27

d12

-3.28

�d12

0 d1210 �d121

0

d12

-0.03

�d12

0

d1220 �d122

0

Table 4. Results of adjustment scheduling obtained by di�erent methods.

Method Hard and softconstraints

DBS Objective CPU (s)Z3 Z4 Z5 Z6

GA 0 1:00e+ 3 0 54.13 1:00e+ 3 1:49e+ 4 32GASA 0 1:00e+ 3 0 4.50 1:00e+ 3 1:51e+ 4 161PSO 0 1:00e+ 3 0 0.05 1:00e+ 3 1:50e+ 4 35

Figure 5. Simple test network.

of 5 units between the transportation capacity anddemand;

2. The upper bound is the condition in which �approaches zero. This condition means that we canadjust the respective plans as long as the largestobjective function can be achieved;

3. The largest di�erences between the algorithms cor-respond to the CPU time. GA can search for anoptimal solution in 32 s, but similar results costGASA and PSO approximately 161 s and 35 s,respectively. Figures 6 and 7 depict the plots ofthe objective value versus the iterations and therequired time of each algorithm, respectively, toobtain the best solution; the y-axis represents theobjective function and x-axis denotes, respectively,the corresponding generations and computationaltime. Clearly, GA is a good choice.

5.2. E�ect of hard and soft constraintsIn this section, the impact of a sensitive segmentcapacity and � variations on the coordination results

Figure 6. Genetic Algorithm (GA) convergence curve forthe sample network.

for the model is explored. From Figure 8, we can seethat when the sensitive segment capacity variability(such as for segment #6) and � value are at a highlevel, the results become similar. Due to the capacitylimit e�ect, all the conditions in which the capacity ofSegment #6 is lower than 30 will have a lower levelof objective value irrespective of the value of �. Thenetwork bottleneck section can again be consideredfor further explanation. It is indicated that hardconstraints imply a penalty of M times on exceedingcapacity, which has a signi�cant negative impact onthe objective value. Thus, the model tends to avoidconstraint penalties.

Next, an attempt is made to �x the capacity of


Figure 7. Time required by each algorithm to obtain itsbest solution.

the sensitive segment #6 to be 25 and examine theimpact of the key parameter �. Based on the discussionin the previous section, the model tends to avoid thesigni�cantly negative e�ect resulting from constraintpenalties. From Table 5, we can see that the DBSreasonably exhibits an increasing tendency along withthe increase in �. It can be expected that the DBSexhibits growth regularity in a reasonable range of �.

Table 6 shows the impact of the key parameters

Figure 8. Illustration of the impact of sensitive segmentand parameter �.

on the DBS in case of insu�cient segment capacity.Here, we �x the capacity of key segment #6 to 50and examine another notable e�ect of �. When thecapacity of segment #6 is su�cient, the hard andsoft constraints do not exert any in uence. Theresults show that at lower � (equal to 75{125), the�nal coordinated plan can be used to obtain extrapro�t by adjusting the original plans. Inversely, at ahigher �(� � 150), extra pro�t cannot cover the DBS.Therefore, the DBS is 0 and the objective is stable

Table 5. Impact of � on solutions (capacity of segment 6 is set to 25).

Beta Objective Hard and softconstraints

DBS CPU time(s)Z3 Z4 Z5 Z6

75 1.63e+04 0 375.2 0 0 375.2 63.2

100 1.60e+04 0 500.2 0 0 500.2 63.5

125 1.56e+04 0 625.4 0 0 625.4 64.1

150 1.54e+04 0 750.2 0 0 750.2 63.9

175 1.53e+04 0 875.7 0 0 875.7 62.8

200 1.49e+04 0 1001.3 0 0 1001.3 32.7

225 1.47e+04 0 1125.7 0 0 1125.7 33.2

250 1.44e+04 0 1252.0 0 0 1252.0 39.0

275 1.42e+04 0 1376.1 0 0 1376.1 48.1

300 1.38e+04 0 1501.0 0 0 1501.0 48.9

325 1.37e+04 0 1626.1 0 0 1626.1 43.4

350 1.35e+04 0 1751.3 0 0 1751.3 57.4

400 1.28e+04 0 2001.5 0 0 2001.5 52.6

500 1.20e+04 0 2501.4 0 0 2501.4 55.0

600 1.10e+04 0 3001.1 0 0 3001.1 51.4

700 9.60e+03 0 3502.0 0 0 3502.0 51.8


Table 6. Impact of � on solutions (capacity of segment 6 is set to 50).



75 2:13e+ 04 0 1496.7 746.7 1503.7 1495.7 34.5100 1:98e+ 04 0 1003.3 0 1003.3 1003.3 36.5125 1:90e+ 04 0 785.9 0 786.0 785.9 37.9150 1:90e+ 04 0 0 0 0 0 38.4175 1:90e+ 04 0 0 0 0 0 39.4200 1:90e+ 04 0 0 0 0 0 37.0225 1:90e+ 04 0 0 0 0 0 36.4250 1:90e+ 04 0 0 0 0 0 37.1

Table 7. Results for the impact of supply and demand relation.



Overdemand 1:90e+ 04 0 2:50e+ 03 1:25e+ 03 0 2:50e+ 03 32.5Oversupply 1:63e+ 04 0 2:51e+ 03 0 2:49e+ 03 2:49e+ 03 32.4

at 1.90E+04. The coordinating results represent thetradeo� results between the extra income and DBS.

5.3. Relationship between production anddemand

Finally, we examine the e�ect of various combinationsof supply and demand scales (Table 7). In case ofoverdemand, the demand amount is 1.5 times that ofthe original scenario in the test network. Inversely,the supply amount is 1.5 times. It is reasonable toincrease the number of products to coordinate plans incase of overdemand. Figure 9 shows the adjustmentrange. The circles in the graph express the decisionvariables, and the length of the vertical lines representsthe adjustments of the decision variables. For example,the graph describing �dim and dim has two points andtwo vertical lines. The two points represent a11 anda12. In case of oversupply, a11 = a12 = 1:5�40 = 60.The two vertical lines describe the adjustment directionand size. The direction of the lines is downward,indicating that d11 = d12 = 10.

6. Case study

The Shenhua Group is the world's largest coal supplierin China, and its integrated operation mode is veryrepresentative in the integrated supply chain. Mul-tiple cooperative units participate in the integratedoperation such as coal production branches, railwaycompanies, ports companies, and power plants. How-ever, the coordination problem becomes increasinglycomplicated since more con icts occur with rapidexpansion of business scale. In order to provide amore scienti�c and e�ective solution for practical work,Shenhua Group is adopted here as a case study.

Figure 9. Optimal coordination results for the testnetwork: (a) Oversupply and (b) overdemand.


Figure 10. Asset distribution map of Shenhua Group in China.

From Figure 10, we can see that six coal produc-tion branches located in Shanxi Province and two ownport companies are involved in the case study. Multipleself-owned railway lines connect production places anddistribution regions. Coal is also consumed in its ownpower plants and other social ports and power facilities.The relevant parameters are presented in Tables 8{10.It should be noted that the upper and lower boundslisted in Table 9 are considered equal in our study,which is also entirely realistic.

Table 8. Information for production branch i.

iCi

(104yuan)Ai

(104ton)

�Ai(104ton)

Ti(104ton)

1 2515 40 200 3002 7522 40 200 3003 3342 40 200 3004 4320 40 200 3005 3077 40 200 3006 1270 40 200 300

Table 9. Production plans from coal mine i for type m.

m

i 1 2 3

1 45 0 45

2 0 50 40

3 69 0 50

4 50 54 0

5 40 55 0

6 0 55 45

Table 10. Variable production cost per unit of coal forcoal mine i and type m.

m

i 1 2 3

1 169 0 129

2 0 180 109

3 106 0 145

4 126 108 0

5 109 138 0

6 0 117 95

Without loss of generality, the demand size is theaverage value of the historical sale data in practice. Weset:

[Bjn; �Bjn] = [30; 30]; [0; Yjn] = [0; 40]; [Bjmn; �Bjmn]

= [20; 20]; [0; Tjmn] = [0; 30]:

The other parameters are de�ned according to opera-tional experience:

Tim = 100; cjm = 4:67; � = 125:

The results for a practical setting are given in Fig-ure 11. The network in Figure 11 presents a simplediagram of the chart presented in Figure 10.

The population size is 100 and the iterationterminates 500 times. The crossover and mutationrates are 0.90 and 0.10. From Figure 12, we can see thatthe trajectory of the hybrid of constraints and DBSterminates after 500 generations in 12.2 min. However,


Figure 11. Practical presentation for operational plan in daily management.

Table 11. Coordination result for the network illustrated in Figure 10.

Method Hard and softconstraints

DBSObjective CPU (min)

Z3 Z4 Z5 Z6

GA 0 4:04e+ 004 0 6:50e+ 004 2:52e+ 004 1:0050e+ 005 12.2

Figure 12. Trajectory of the hybrid of hard and softconstraints.

we can get an approximate optimal solution after 50generations when making quick decisions is essential.The improvement of the objective is not notable withthe increasing number of iterations. The subgraph onthe left shows the iterative process of the hard and softconstraints before 60 steps, and it is noted to approach0 rapidly. The DBS curve for 60{500 steps is zoomed in

in the right subgraph, and the objective contributionsare listed in Table 11.

7. Conclusions

The integrated coordination supply chain planningproblem has become increasingly crucial since con ictscommonly exist among the respective plans from allbranches. The contribution of this paper is theproposal of a scheduling model based on hard andsoft constraints. On the one hand, we attempted tomaximize the company pro�t and minimize the gapbetween the proposed plans and the coordinating plans.Due to the e�ect of the DBS, the problem can be seenas a tradeo� strategy between the increased pro�ts andcost of coordinated adjustment.

The results for the Shenhua Group case suggestthe following practical observations. The con ictresolution strategy that should be employed is the onethat (1) functions by replacing high-intensity laborand experience-dependent leadership decision-makingmechanisms and (2) promptly identi�es the marginalcontribution of each branch in the supply chain withouttedious and repetitive statistical analysis. We com-pared several algorithms and all of them can obtainan optimal and similar solution. However, rapiddecision response in a short time is still a challenging


topic. In particular, the rescheduling method with theconditions of exible information such as uctuationof market demand, the weather condition, and policychange should be considered in further studies.

Funding

This work was supported in part by the NationalNatural Science Foundation of China under Grant71801160, in part by the China Postdoctoral ScienceFoundation under Grant 2018M641711, and in partby a project from the Department of Education ofLiaoning Province under Grant WQGD2017024.

Acknowledgments

The authors would like to thank the Shenyang Univer-sity of Technology for enabling us to participate in theYoung Teacher Training Program.

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Biographies

Yang Jiang was born in Shenyang, Liaoning, Chinain 1986. He received his BS from the Dalian JiaotongUniversity in 2009, his MS from Beijing JiaotongUniversity in 2011, and his PhD from Beijing Jiao-tong University in 2014. From 2015 to 2017, hewas a Research Assistant at the school of Economicsand Management, Tsinghua University, China. Hisresearch interests include the management of railwaylogistics in relation to intermodal transportation usingmathematical modeling methods. He is currently atthe Shenyang University of Technology. In 2018, hereceived a research project grant from the NationalNatural Science Foundation of China and funding fromChina Postdoctoral Science Foundation.

Qi Xu is from Yunnan province, China. He receivedhis PhD degree from Beijing Jiaotong University in2011. He is currently at the Beijing Jiaotong Univer-sity.

Yao Chen was born in Fuzhou, Jiangxi, China in 1993.He received his BS degree and PhD degree from BeijingJiaotong University in 2013 and 2018. He is currentlya postdoctoral research fellow at National Universityof Singapore. His research interests include operationresearch on public transit and car-sharing systems.

developing a joint supply chain plan for the coal industry...

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